Finite state bilaterally deterministic strongly mixing processes
type: Item
instance of: scholarly article
title: Finite state bilaterally deterministic strongly mixing processes
zbMATH Open document ID: 0874.60032
DOI: 10.1007/BF02761036
author: Meir Smorodinsky
author: Robert Burton
author: Manfred Denker
published in: Israel Journal of Mathematics
publication date: 1997-11-10T00:00:00Z
review text: Let \(\{X_n\}_{n\in\mathbb{Z}}\) be a two-sided sequence of i.i.d. random variables with finitely many states. The authors construct explicitly a factor sequence \(\{Z_n\}_{n\in\mathbb{Z}}\) of the above sequence that has finitely many states, and is \(\alpha\)-mixing and bilaterally deterministic, i.e. each of the \(Z_n\)'s is measurable w.r.t. the double-tail \(\sigma\)-field generated by \(\{Z_n\}_{n\in\mathbb{Z}}\). This result complements an earlier example by \textit{R. C. Bradley} [Trans. Am. Math. Soc. 294, 233-241 (1986; Zbl 0595.60040)] of a \(\rho\)-mixing, bilaterally deterministic process with continuous state space.
Mathematics Subject Classification ID: 60G10
zbMATH DE Number: 952560
zbMATH Keywords: stationary sequence
zbMATH Keywords: strong mixing
zbMATH Keywords: two-sided tail
zbMATH Keywords: bilaterally deterministic
reviewed by: R. L. Schilling
MaRDI profile type: Publication
cites work: A Bilaterally Deterministic ρ-Mixing Stationary Random Sequence
cites work: Q3739966
cites work: Q4086515
cites work: Every transformation is bilaterally deterministic
cites work: A CENTRAL LIMIT THEOREM AND A STRONG MIXING CONDITION
cites work: A partition on a Bernoulli shift which is not weakly Bernoulli
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description: scientific article; zbMATH DE number 952560